{"id":187744,"date":"2025-02-06T06:04:23","date_gmt":"2025-02-06T06:04:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187744"},"modified":"2025-02-06T06:04:25","modified_gmt":"2025-02-06T06:04:25","slug":"which-of-the-following-column-formulas-is-applicable-to-cast-iron-columns","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/which-of-the-following-column-formulas-is-applicable-to-cast-iron-columns\/","title":{"rendered":"Which of the following column formulas is applicable to cast iron columns"},"content":{"rendered":"\n

Which of the following column formulas is applicable to cast iron columns?<\/p>\n\n\n\n

a) Euler\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s formula
b) J.B.Johnson\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s formula
c) Secant formula
d) Straight line formula<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer:<\/h3>\n\n\n\n

b) J.B. Johnson\u2019s formula<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

Cast iron columns are typically short and stocky rather than slender, meaning they fail primarily due to crushing rather than buckling. This behavior makes Euler\u2019s formula<\/strong> unsuitable because Euler\u2019s formula is used for long, slender columns<\/strong> that fail due to elastic buckling<\/strong>. Cast iron, being brittle, does not exhibit significant elastic deformation before failure. Instead, it fails suddenly under compressive stresses.<\/p>\n\n\n\n

To account for the inelastic buckling and crushing characteristics of cast iron columns, J.B. Johnson\u2019s formula<\/strong> is used. This formula is an empirical modification of Euler\u2019s formula that considers both elastic and inelastic buckling effects, making it suitable for columns with intermediate slenderness ratios<\/strong>. The formula is expressed as:<\/p>\n\n\n\n

[
P_{cr} = \\frac{\\sigma_c}{1 + \\frac{\\sigma_c}{\\pi^2E} \\left(\\frac{L}{K}\\right)^2}
]<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • ( P_{cr} ) = Critical load<\/li>\n\n\n\n
  • ( \\sigma_c ) = Compressive stress at failure (yield stress for ductile materials or crushing stress for brittle materials)<\/li>\n\n\n\n
  • ( E ) = Modulus of elasticity<\/li>\n\n\n\n
  • ( L ) = Effective length of the column<\/li>\n\n\n\n
  • ( K ) = Radius of gyration<\/li>\n<\/ul>\n\n\n\n

    This formula transitions between Euler\u2019s buckling theory for long columns and Rankine\u2019s crushing theory for very short columns, making it more applicable to cast iron columns, which are generally short or intermediate in length<\/strong>.<\/p>\n\n\n\n

    Why Not Other Formulas?<\/h4>\n\n\n\n
      \n
    • Euler\u2019s Formula<\/strong> is only valid for long, slender columns where buckling is elastic, which does not apply to brittle cast iron.<\/li>\n\n\n\n
    • Secant Formula<\/strong> is used for eccentrically loaded columns, which is not the primary concern for cast iron columns.<\/li>\n\n\n\n
    • Straight Line Formula<\/strong> is a simplified empirical approach but does not accurately describe the transition between buckling and crushing, which J.B. Johnson\u2019s formula does.<\/li>\n<\/ul>\n\n\n\n

      Thus, J.B. Johnson\u2019s formula is the most applicable for cast iron columns.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

      Which of the following column formulas is applicable to cast iron columns? a) Euler\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s formulab) J.B.Johnson\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s formulac) Secant formulad) Straight line formula The Correct Answer and Explanation is : Correct Answer: b) J.B. Johnson\u2019s formula Explanation: Cast iron columns are typically short and stocky rather than slender, meaning they fail primarily due to crushing rather […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-187744","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187744","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=187744"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187744\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}